$\mathcal{N}=2$ Super-Teichmüller Theory

Abstract

Based on earlier work of the latter two named authors on the higher super-Teichmueller space with $\mathcal{N}=1$, a component of the flat $OSp(1|2)$ connections on a punctured surface, here we extend to the case $\mathcal{N}=2$ of flat $OSp(2|2)$ connections. Indeed, we construct here coordinates on the higher super-Teichmueller space of a surface $F$ with at least one puncture associated to the supergroup $OSp(2|2)$, which in particular specializes to give another treatment for $\mathcal{N}=1$ simpler than the earlier work. The Minkowski space in the current case, where the corresponding super Fuchsian groups act, is replaced by the superspace ${\mathbb{R}}^{2,2|4}$, and the familiar lambda lengths are extended by odd invariants of triples of special isotropic vectors in ${\mathbb{R}}^{2,2|4}$ as well as extra bosonic parameters, which we call ratios, defining a flat ${\mathbb{R}}_{+}$-connection on $F$. As in the pure bosonic or $\mathcal{N}=1$ cases, we derive the analogue of Ptolemy transformations for all these new variables.

v2: 41 pages, published version

References in corpus (1)

• Decorated Super-Teichmüller Space

Cited by in corpus (8)

• Super McShane identity
• An Expansion Formula for Decorated Super-Teichmüller Spaces
• On Ramond Decorations
• Flat $GL(1|1)$-connections and fatgraphs
• An Introduction to Supersymmetric Cluster Algebras
• Some Generalizations of Mirzakhani's Recursion and Masur-Veech Volumes via Topological Recursions
• Super-Teichmüller spaces and related structures
• Super Riemann surfaces and fatgraphs